High frequency electron discharge device and system



May 21, 1957 E. D. MCARTHUR HIGH FREQUENCY ELECTRON DISCHARGE DEVICE AND SYSTEM Filed Jan. 4, 1952 5 Sheets-Sheet l Om a Fig.3.

I2 34- 567 6 SNHIZHHIF Ln 0 ll n [fiventorz Eime'r D. Mc Arthur:

K2 me His Attorney.

May 21, 1957 E. D. MOARTHUR HIGH FREQUENCY ELECTRON DISCHARGE DEVICE AND SYSTEM Filed Jan. 4, 1952' 5 Sheets-$heet 2 Fig.4. MODULATION mnsx 0F INPUT cums FigsA.

.5313 2. #288123 455235? an 5562mm- .1 In 1-2 I4 1.; u 2.0 p-suucnma PARAMETER [254.5672; snub/3141s Inventor: Elmer D- Mc Arthur, by /Q..4 4.

His Attorney.

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4 fUZmUE n 3 EN y 1957 E. D. MGARTHUR 2,793,316

HIGH FREQUENCY ELECTRON DISCHARGE DEVICE AND SYSTEM Filed Jan. 4, 1952 5 Sheets Sheer, 3

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Inventor; Elmer D. 'Mc Arthur: by 2 6 4. m

His Attorney.

May 21, 1957 E. D. MOARTHUR HIGH FREQUENCY ELECTRCN DISCHARGE DEVICE AND SYSTEM Filed Jan. 4, 1952 5 Sheets-Sheet 4 Inventor: Elmer D. Mc APthLL His Attorney.

May 21, 1957 E. D. MCARTHUR 2,793,316

HIGH FREQUENCY ELECTRON DISCHARGE DEVICE' AND SYSTEM Filed Jan. 4, 1952 5 Sheets-Sheet 5 F a m.

lnlllqllllll-lfllllllllllll Inventor: Ehner D. Mc Arthur; by 2 .01 4 m His Attorney.

United States Patent HIGH FREQUENCY 'ELECTRQN DFSCHARGE DEVICE AND SYSTEM Elmer D. McAr-thur, Schenectady, N. Y assignor to General Electric Company, a corporation of New tori:

Application January 4, 1952, Serial No. 255,014 23 Claims. (Cl. $15-$44) This invention relates generally to the translation of electromagnetic energy and, in particular, to novel methods and devices utilizing both space charge control of current flow and velocity modulation phenomena for the generation and amplification of electromagnetic waves.

The progress of the electronics industry toward the use of higher and higher frequency electromagnetic waves is, of necessity, dependent upon the development of methods and devices for the translation of such electromagnetic waves. The term translation as employed herein includes both the generation and amplification of electromagnetic waves. Conventional electron discharge devices, or vacuum tubes as they are commonly identified, are limited to low frequency operation by such factors as the inductance of leads to the tube elements, the losses by radiation from the tube structure and connecting leads, etc.

One of the more successful types of high frequency electromagnetic Wave tubes, described in my article in Electronics, vol. 18, pp. 98-402 (February 1945), is a special space-charge vacuum tube, usually referred to as the disk seal tube. This tube is an outgrowth of the Wellknown low frequency, cylindrical electrode vacuum tube and is chiefly identified by its planar electrode structure which enables very small interelectrode spacings. The disk-seal tube depends for its operation, as does the low frequency vacuum tube, upon space charge control of current fiow to deliver an alternating current to an output circuit. Space charge control of current flow is defined as the varying or modulating of electron flow from a cathode .by changing the electric field at the surface of the cathode. In the higher frequency or microwave range, however, deleterious effects, occasioned by the time required for electrons to travel between electrodes and commonly known as transit time effects, occurand necessitate the reduction of interelectrode spacings to preserve the space charge control current modulation characteristics of the tube. In some instances, the interelectrode spacings of the disk-seal tube are of the order of 0.1 mm. or smaller. Consequently, the disk-seal tube is limited by the mechanical difficulties inherent in maintaining the requisite close manufacturing tolerances.

The velocity modulation tube, sometimes referred to as the klystron, is another type of high frequency electromagnetic wave tube in which the comparatively long transit times encountered in the microwave frequency spectrum are utilized to advantage, rather than being minimized as in the disk-seal tube. One of the more familiar forms of the klystron comprises an electron gun which produces an accelerated beam of electrons having a constant velocity and density. This constant velocity and density beam is directed through the interaction gap of an input resonator where a high frequency excitation voltage gives each electron an additional acceleration-positive or negative-depending upon the phase and magnitude of the gap voltage during passage of the respective electrons. The beam, which now contains electrons of various "ice velocities, is directed through a drift space or region essentially free from external electric fields in which the variations in velocity create density modulation or electron grouping. The electron groups or bunches are then caused to traverse the interaction gap of an output resonator to excite it into oscillation and deliver power to a load. Since the velocity modulation is applied only after direct current acceleration of the electron beam to 'a relatively high average velocity, the requirements for electrode spacings in the input gap are much less severe than in the disk-seal tube. However, as is well known to those skilled in the art, the ideal efliciency of a two-resonator klystron is 58% and is much lower in practice where circuit and beam loading losses are present. With the socalled'multi-gap klystron, the ideal efiiciency may be increased to about 74%, but the additional structural complexity of the device tends to offset this advantage materially to those concerned with its manufacture and use. An extensive discussion of klystron characteristics, as well as those of the disk-seal tube, may be found in the Radiation Laboratory Series, volume 7, entitled Klystrons .and Microwave Triodes and authored by Donald R.

both space charge control and velocity components and then directed through a drift space or essentially elec- ,tric field-free region. After its passage through the drift space wherein density modulation or bunching occurs as a result of the initial velocity modulation, the bunched electron stream is caused to excite anoutput circuit whereby power may be delivered to a load.

A variety of input electrode-structures may be. employed to obtain the initial space charge control and velocity modulation of the invention. In each case, however, enhanced efi'iciency is obtained by arranging the input electrode structure, in conjunction with operating conditions, to secure a predetermined phase angle between the initial current modulation component provided by space charge control and the total transit time or transit angle of the electrons from the inception of the space charge control to the end of the drift space. The greatest enhancement of efficiency occurs when the time-varying total transit angle leads the space charge control current component in phase by or when the phase angle equals +1r/2, and this is true regardless of the form of input electrode structure and regardless of whether the fundamental or a given harmonic of the input frequency is utilized. Further enhancement of efficiency is realized by also arranging the invention-to obtain a predetermined value of a bunching factor-which is a measureof the degree ofbunching of the electron stream as it leaves the drift space. As a specific example, for sinusoidal modulation of the electron current by the space charge control component, maximum efficiency for'fundamental frequency occurs when the bunching factor equals 1.47 and the above-mentioned phase angle equals +1r/2. Moreover, the invention makes it possible to secure very high efiiciencies at harmonic frequencies, thereby enabling the progress of the electronics industry toward the use of higher and higher frequencies.

The features of the invention desired to be protected are set forth in the appended claims. The invention itself, together with further objects and'advantages thereof, may best be understood by reference to the following specification taken in connection with the accompanying drawings in which Fig. l is a simplified schematic useful in explaining the invention; Figs. 2, 3, 3A, 4, 5 and 6 are graphs which are employed to illustrate the interdependence of various parameters of the invention; Fig. 7 is another simplified schematic useful in explaining a diode input structure according to the invention; Fig. 7A is a graph illustrating the efiiciency of a diode input structure of the invention; Fig. 8 is a simplified section view of a diode input device according to the invention; Fig. 9 is a schematic illustration, partly in section, of feedback means which may be employed in conjunction with the devices of the invention; Fig. 10 is a simplified perspective view of another embodiment of a diode input device utilizing wave guides according to the invention; Fig. 11 is a sectionalized representation of another embodiment of the invention especially adapted for high power applications; and Fig. 12 is a section view of a further embodiment of the invention in which a triode input structure is utilized.

As has been outlined above, the disk-seal tube and the klystron or velocity modulation tube obtain their operational characteristics from contrasting physical phenomena, i. e., space charge control and velocity modulation of an electron stream. For this reason the analytical treatments of these two general microwave tube types have been mutually exclusive and basically divergent. According to the present invention, however, there are provided novel methods and devices wherein an electron stream is initially modulated at the same input frequency with both space charge control and velocity modulation and then directed through a drift space; consequently, the heretofore known analytical treatments are not applicable. The following description of the present invention, therefore, contains an analysis treating the requisite space charge control and velocity modulation components of an electron stream. As will be seen, this analysis presents a theory which enables a clear and complete description of the invention and also defines the manner in which the various parameters must be arranged to secure the many advantages of the invention.

For an understanding of the present invention, reference may be had to the simplified representation of Fig. 1 in which the numeral 1 denotes a drift space or fieldfree region having a length L. This representation will be employed in the ensuing analysis, along with certain assumptions, to facilitate the derivation of conditions which must be observed according to the invention.

To begin with, it will be assumed that an electron stream is generated in some fashion and directed through drift space 1 from left to right as indicated by arrow 2. It will also be assumed that the electron stream has both velocity modulation and space charge control current modulation components prior to its entrance into drift space 1. In order to maintain the consideration of these components of the electron stream in the most general form, the instantaneous output current, caused by the bunched electron stream at the time of its emergence from drift space 1, will be designated i and defined by the following Fourier series:

where A is the direct current component of output current, t is the time of arrival of an electron at the exit end of drift space 1, and A B A B,, An and En are coeflicients of the alternating components of the output current.

The generalized coefficients A71. and En are found by It is apparent, however, that the integrations of Equations 2 and 3 cannot be performed directly because nothing is known about i and t Nevertheless, other considerations permit a modification of these equations whereby the integrations may be computed.

Consider a small element of charge dq of the electron stream at any arbitrarily positioned plane JCa. in the region preceding the entrance to drift space 1. This charge dq is defined as the charge which is contained in a section of the electron stream taken perpendicular to the direction of motion; the thickness of the section will be termed dx. Since the electron stream has been assumed as moving at some velocity, the moving charge dq constitutes an electric current, flowing through plane xa, which by definition is:

i d where die. is the time required for the electrons carrying the charge to move through the distance dx at velocity Ila. In other words,

where lug. is the instantaneous velocity of the electrons while passing through plane 3611.

Consider next the same charge at a later time and, in particular, examine its status at the time t that it crosses a plane x at the exit end of drift space 1. To obtain generality, we will assume that the electron veloc ity has, for some reason, changed to another value u,. The time for the electrons to cross the same distance dx now has a new value a t such that and the same amount of charge dq moving at the altered velocity a defines a different value of electric current at the exit end of drift space 1, viz., by definition:

If the quantity of electric charge is conserved, i. e., no electrons are lost or destroyed, we may consider the behavior of an amount of charge dq at the plane x and the subsequent behavior of the identical charge increment at the plane x Since no provision has been made for electrons moving anywhere but into and out of drift space 1, conservation of charge must exist. Hence, from Equations 4 and 7 respectively, we find dq=i dt (8) and dq i dt whereby i dt =i dt 10 The above rationale may be used with reference to an earlier time increment a't during which the charge dq crosses an arbitrarily positioned plane x Consequently, we may write:

This running equality obviously can be extended to as many planes as desired if such planes are assumed to be perpendicular to the direction of travel of the electron stream. As will be shown hereinafter, employment of this equality series in connection with Equations 2 and 3 facilitates the desired integrations.

We may now direct our attention to further specification of the electron current preceding its entrance into drift space 1. The instantaneous value of current of the electron stream will be designated i at time t when the electrons cross an arbitrarily positioned plane x The symbol x merely identifies the arbitrarily positioned plane and may or may not represent the distance from-the plane .vc to plane 2a,, which is located-at the entrance of drift space 1. The current i will be assumed to have alternating and direct current components of arbitrary magnitude and to be defined by the following expression:

i =r,+1r sin m 7 12 where l =reference axis for the sine wave representing the A. C. component, I =magnitude of alternating current component measured from Ir, and t =tirne at which electron giving rise to i cross the plane x with the added provisions that i is never negative and that whenever a negative value for i is indicated by'Expression 12., i shall be assumed to be zero. g a

Expression '12 will be readily recognized as the form of the equati'onfor the fundamental component of current flow in a diode, t'riodeo'r tetrode, which arises from the impressed direct and sinusoidal voltag-es. A-s'iscustomary in the treatment of triode'syseveralspecificwave forms which are of particular interest may be derivedfi These are the well-known Classes A, B and C conditions of operation. In the Class Acondition, the fundamental current wave form consists of a direct current component and a superimposed alternating current component of such amplitude that I is equal to or less than I1- and linearly related thereto, whereby Expression 12 may be written:

i =I (1-|-M sinwt (.13)

where 1 :1 and V The parameter M is, as may be seen, the ratio of the fundamental of the space charge control component iof electron current to the average current and will be referred to hereinafter as the modulation index of input current. For the Class B condition, Ir=0 and from EX- pression 12 i =l sin wt (15) For the Class C condition, Ir is negative and from Expression 12 In Class A operation the current may be instantaneously zero at wr =31r/2 when M :1. However, the current is zero nowhere else in each cycle, and the full sine wave is displayed. In Class B operation the current wave shape is one-half a sine wave from wt =O to wt =vr and zero 1 :1 sin wt -I from wt =1r to wt 21r. In Class C operation the current is positive during an angle of less than 180 and is zero during the remainder of each cycle.

While the present invention contemplatest-he employment of all three conditions of operation, the remaining portion of the analysis will deal in detail only with the "Class A condition of the space charge control component.

For the other conditions, as those skilled in the art will realize, the analytical procedure is the same as in-Class A-except that the various integrals are evaluated not from O to 211- but only for the angular duration of the actual current flow.

One further factor must yet be specified to permit the calculation of integral Equations 2 and 3, i. e., the time z at which an electron, which began its journey at time t arrives at the plane x, at the exit end of drift space 1. To obtain this, we shall assume that the electron velocity u, at the entrance to the drift space is of the very general form:

u =u ,[1+p sin (wt +a (17), where tr l-average velocity.

. p =ratio of the amplitude of the sinusoidal component of velocity to the average velocity, with the provision that0 1.' I j the alternating velocity conimay be equated to Tat, the average transit time through drift space 1, :whereby by substitution into Equation 19, we obtain T =I [1-;a sin (wt -l-u fl '(20) The total elapsedtimefrom plane x, to x is where T is the time spent by an electron in traveling from plane x, to the entrance to drift space 1; hence :,=r +T +T or by substitution of Equation 20 v v i v =t +T -|T ,[l12 sin (wt +ot Y (23) Multiplying Equation 23 by 0) gives wf =wt +wT +wT w p sin (wtb-l-ai) (24) At this juncture we must considerthe transit angle wT to obtain an expression for t in terms of t It'is Well known that a-direct integration of the equations of force upon an electron in a discharge path such as we are here considering results in an algebraic expression for the transit angle wT,, of an electron moving from plane x, to x,, which is nearly useless for further completely rigorous analysis. Nevertheless, this expression may, for present purposes, be changed to the following form:

where wT is the transit angle from x to x, in the absence of an alternating velocity component, and m and m are coefficients of the trigonometric functions. This is an approximation which represents the true equation with an error generally not more than a few percent. Examples will appear hereinafter. Substituting Equation 25 into 24 and expanding the trigonometric term, we obtain:

w! =wt +wT +m sin wt +m cos v wt +wT P wT sin wt COS a' p wT' cos wt sm a Collecting the trigonometric terms Equation 25b can be written as:

As will be shown hereinafter, the size of the functions #1,, 1p, and 1, 1, depend, in a practical adaptation, upon electrode dimensions andoperating conditions and can be determined analytically for any chosen system of electrodes. The parameter p is a bunching factor and a+1r=6 is the phase angle between the space charge control current modulation component and the total transit angle, the full significance of whichwill appear later.

Sufiicient information is now available to permit the computation of Equations 2 and 3. From the running equality (11), we may obtain I i,aft,=i,at (26) and substitute into Equation 2 to secure:

A,,= 1 f"i, sin minder, 27

Replacing wt, by its equality from Relation 25c gives Substituting for i from Equation 13, we obtain In order to simplify, we shall define s= n+ (s s)= fi and substitute into Equation 29 to obtain:

21' AFH [1+M sin in l n s+ Po-"1 Bill @1 1 And by a similar process l o"' fl Sin sons By expansion of the terms in An and B71, and with the use of trigonometric relations, it may be shown that the term rh -w appearing in the sin and cos terms in Equations 32 and 33, respectively, has no effect upon the answer sought at the present, i. e., the magnitude of the nth harmonic of output current i,. Therefore Equations 32 and 33 may be written respectively as:

I 21' -B,.=; 0 [1+Msin is-an cos [(n)(fl-p sin m d s Carrying out the integrations gives:

An -2lo]n(n sin (na)+MIo cos a (36) where the symbol 1 indicates the Bessel function of the first kind. The magnitude of the nth harmonic of alternating output current, Cu, is determined from the following relation:

Cn =A-n +Bn (38) Squaring Equations 36, 37 and substituting into 38 produces, after simplification I 2 ss= o n p)[ ni( J,+ imp) sin a} 39 As will now appear to those skilled in the art, Equation 39 represents the square of the magnitude of the nth harmonic of alternating current output from drift space 1 when an electron stream, which has been modulated with both space charge control and velocity modulation components as specified hereinbefore, is fed into the drift space. From Equation 39 we may obtain the optimum values for the several variables involved; thus we can determine the specific parameters for input electrode structures and circuits and for drift space 1, such being contemplated by the present invention and more fully disclosed hereinafter.

As will be seen, Equation 39 provides a basis for an expression of efficiency. If we define efliciency, 1 in the usual sense as the ratio of input power to output power, we may state that n is the product of Cit/21 and the ratio of peak A. C. output voltage to beam voltage. Thus, to find the value of a for maximum efiiciency we compute the conditionfor which d 0, 2112 To i- From (39) and (40) we have,

(n cos a=O Equation 41 can be satisfied only by cos =0 or oc=;*:1r/2, and this, it should be noted, is independent of the value of n. In Fig. 2 calculations of the variation of the ratio of fundamental output current to average current (for two values of p and for M=1) with respect to a are plotted and reveal that 0t=1r/ 2, produces a maximum while ot=+1r/ 2 produces a minimum. Consequent- 1y, for maximum efiiciency, the angle a must equal 1r/2,

Substituting ct=1r/2 into Equation 39 gives s J, (sp |:1 2) or |0 .|=2m, np)[1+%] (43) Alternatively, by substituting ot=1r/2 into Equations 36 and 37, the same answers may be obtained for An or Bn. Choosing n to be any even integer produces M l .|=2I0J,(np [1+-;] (45) and hence that wi -wt, equals the total transit angle wT, from plane 24 to x,. Therefore, Equation 45a may be expressed as l 0+! S111 fl 'i l o+ sin o'i' Substituting a=-1r/2 into Equation 45b and expanding, we obtain In Fig. 3A, there is shown a plot of the alternating space charge control component of electron current i versus wt and a plot of wT the total transit angle for an arbitrary value of p, versus wt, for ot='-1r/2 and =+-1r/2. As will be observed, the two sinusoids are displaced by 90, the value of the angle a for maximum efficiency. Thus, for maximum efiiciency, the total transit angle wT must lead the space charge control component of electron current by 90. t also appears from Fig. 3A that, for maximum bunching of the electrons at the exit end of drift space 1 and hence for maximum efiiciency, bunches must reinforce the space charge modulationand therefore must be formed about the 1r/2, 51r/2, 91r/2, etc. positions of the i curve. This means that the electrons in the quarter cycle to the left of these points must have their velocities decreased before enteringv drift space 1 since their starting times from wt =0 are earlier while electrons in the quartercycle to the right of these points must have their velocities increased before entering drift space 1 since their starting times from wt =0 are later. Arranging-.thetotal transit angle wT. to vary as illustrated in Fig. 3A produces a maximum effect of this nature.

To find the optimum value of li we compute the condition for d C l' 4 n 0) 0 6) From (43) with 1r/2 substituted form we have,

The largest output current is found, as far as the space charge control component amplitude is concerned, when M=l and for this value of M in Equation 47, the optimum value of u may be obtained from Equation'48 can only be solved by numerical trial and error. It will yield a different optimum value of bunching factor p for each value of n, as is shown in Fig. 3 wherein pm, the optimum value of is plotted against it. At the fundamental frequency, p =l.47, a value which will be used hereinafter for illustrative calculations involving p It has been stated above that the present invention provides methods and devices for the generation and translation of electromagnetic waves in which enhanced eff ciency is obtained. This fact is represented by Fig. 4 wherein efficiency of power conversion at the fundamental frequency is plotted versus p, the bunching parameter. In obtaining this graph, the ratio of peak alternating output voltage to beam voltage has been assumed to equal one, whereby Cn/ 210 from Equation 43 (a: 'rr/2) determines the efiioiency as a function of p and M, the

modulation index. A family of curves for various values:

of M is illustrated to fully display the interrelationships. Dotted line 3 denotes the locus of the efficiency maxima. It is to be specifically noted that with M :1, and =l.47 the highest efficiency of approximately 93% is obtained. When M =0, however, no space charge control component of electron current is present; hence only velocity modulation or klystron action is applied to the electron stream, and the maximum efficiency is about 58%. Thus, the enhanced efficiency, obtained according to the instant invention by employing both space charge control current modulation and velocity modulation of the electron stream, is manifest. In the range of about =0.7 to about =2.0, for example, and for M: 1, the efficiency always exceeds 80%.

With reference again to Fig. 2, the greater efficiency secured by utilization of the invention is further illustrated. While a=1r/2 or 31/2 (0:1r/2 or 51r/2) always produces maximum efiioiency regardless of the value of p and regardless of the value of M, greater efiiciency than that obtained with velocity modulation alone is always realized when 0 a 1r and 1r 0 0 (alternatively, when (Fig.- 2 shows the'variation of the ratio of fundamental output current to average current with respect to a for =1.47, the value-which results in the indicated maxiexceeds 58%. The deliberate employment of velocity modulation and space charge control current modulation in a predetermined phase with respect to the total transit angle variation is therefore critical in the attainment of the advantages of the invention. In practice, since maximum efliciency isuniformlydesirable, the use of ot=--1r/2 and 0=+7r/2 in every application of the invention is most important.

In Fig. 5, the wave shape of the output current secured according to the invention is represented. Curve 6 illustrates the variation of relative beam current with respect t0'wt i// for =1.47 Iand'M :1; curve 7 represents average current. For comparison purposes, curve 8 for M :0 is included. Particular attention is directed to the fact that the relative beam current reaches zero for all practical purposes at about wf rl/ =i when M :1 (curve 6) while it never can reach zero when M =0 (curve 8). Thus holes or spaces are actually produced in the electron stream when space charge control in addition to velocity modulation is utilized as specified by the invention. This provides a clear interpretation of the enhanced efi-lciency of the invention, because it is easily recognized that greater efficiency arises as the electron stream is increasingly bunched to cause the electron current to approach or reach zero in between bunches.

An important facet'of this invention is the provision of methods and devices for securing heretofore unobtainable high efficiencies at harmonic frequencies. Fig. 6 represents the variation of maximum efiiciency, with respect to harmonic ratio, n. As will be observed, the maximum efficiency remains over 50% even for the 15th harmonic of the input frequency. While the foregoing discussion has dealt chiefly with the Class A condition of the space chargecontrol component, the efliciency at the tenth harmonic for Class B operation, which is within-contemplation of the invention, has been calculated to be 97%. With Class C operation, also envisaged, efficiencies are still higher. Therefore, the present invention has especial importance when harmonic frequencies are utilized.

It will now appear that, although the values of a, 0 and p which result in maximumefficiency have been obtained from the foregoing general analysis, these factors depend upon physical parameters in a way which is different in detail for each form of electrode structure and operating conditions employed for the input to drift space 1. Therefore, a, 0 and p must be related to specific electrode structure and operating conditions before the physical parameters can be calculated. The following analysis presents the calculation'of the physical parameters for a diode input to a drift space.

Reference may now be had to the simplified illustration of Fig. 7 in which a drift space 10 is represented as having a diode input. In this figure plane 11 may be considered a cathode and plane 12 an electrode, which may be in the form of a grid, between which is defined an input interaction gap 13 having a width S. Following plane 12 is field-free drift space 10 having a length L and being terminated by a plane 14. Plane 15 may be considered as an anode whereby planes 14 and 15 together define an output interaction gap 16. The output current which flows in gap 16 will be computed for this electrode system by following the same pattern and pro-.

cedure used in the previous general derivation. Also the justification for the assumptions used in the general derivation will become evident as the calculations proceed.

Assume that a suitable circuit, such as a cavity resonator (not shown), is connected to cathode 11 and electrode 12 and that the circuit, together with a suitable power supply and high frequency signal source, provides an input gap voltage V=Vo+V1 Sin wt=Vo (l-I-K sin wt) (49) where Vo=beam voltage or average potential difierenee between 11 and 12, and

Vi=amplitude of alternating potential difference between 11 and 12.

This voltage applied across the input gap would, at low frequency, produce a current flow where i',,=instantaneous current amplitude at plane 11.

It is well known that at microwave frequencies when the time of transit of an electron across a gap such as gap 13 is of the order of the period of the alternating voltage thereacross, the net circuital current is considerably modified as a result of the change in electrode potential which occurs while electrons emanating from the cathode are in transit. For present purposes, however, it is not necessary to know the net circuital current; all that is needed is a knowledge of what the current is at any one plane parallel to cathode plane 11. In particular, it is desirable to ascertain the instantaneous electron conduction current leaving cathode plane 11. As will appear from the following reasoning, this may be determined from Equation 50.

Even at the highest microwave frequencies, e. g., 40,000 megacycles, and for practical current densities, the electric field within input gap 13 changes instantaneously when the gap voltage changes. That is to say, any change in gap voltage is accompanied by a proportionate and simultaneous change in the electric field close to the cathode. Now consider a plane (not indicated in Fig. 7) located in space parallel to and an infinitesimal distance AX in the +X direction away from cathode plane 11. The potential at this plane is determined by the gap voltage and the space charge distribution which is assumed to be essentially the same as it is at low frequency. This latter assumption takes into account all of the usual space charge effects but neglects the second order modification of space charge distribution which results when the electron transit time in gap 13 is comparable to the period of the alternating voltage; therefore, with this reservation the potential of the AX plane is that which is computed in the usual way from the well-known low frequency space charge equations. Since the electric field in gap 13 changes instantaneously, the potential of the AX plane must change in conformity with the gap voltage and with no time delay. The position of the AX plane is entirely arbitrary, and AX may be selected so small that the transit time of an electron from cathode plane 11 to the arbitrary plane is entirely negligible regardless of how high the frequency may be. Consequently, the electron conduction current flow through the arbitrary AX plane and from cathode plane 11 must be the same current which would flow if the frequency were very low. Thus, at time t the instantaneous conduction current leaving cathode plane 11 may be computed by Equation 50 even in the microwave spectrum.

In the absence of an alternating voltage across gap 13, the average current in amp./ cm. is

and, hence, from Equations 50 and 51,

i,,=l,, (1+K sin 010 (52) Expanding this expression into a binomial series gives i',,=I,, (1+ Z K sin wt+/;K sin wt+ (53) For present purposes including the determination of the fundamental component of output current which is obtained according to the invention with a device embodying principles illustrated by Fig. 7, only the first two terms of Equation 53 need be considered; neglect of the second order term can be shown to produce an effect of only 2 or 3%. These two terms give the instantaneous current 1",, leaving the cathode at time t'.,:

w l t cos (nwt )dwt 57) Now, with the aid of Equations 51 and 54 the current i, may be calculated from the dimensions of the electrodes and the applied voltages. In order to complete the integrations, however, it is necessary to compute wt' in terms of wt, for the particular electrode system of Fig. 7. This may be done in the ensuing manner.

Neglecting the efiect of space charge, the electric field in gap 13 is and substituting for V from Equation 49 gives 1+K sin wt) 59) or E=E (1+K sin 6: where E =V,,/S

The force on an electron in this field is Xgk 1+K sin wt) (60) where e=eleetnon charge and m= electron mass. Two integrations of Equation 57, with the added conditions that X =X =0 when t=t'., give where u is the electron velocity, and

K sin wt K sin wt] (62) The time at which the electron leaves plane 11 is, as

defined hereinbefore, t It t is defined as the time of arrival of the electron at plane 12, the velocity with '33 which an electron arrives at plane 12 is found from Equation 61 to be eyesore it ponents higher than one, the final solution for all" may be obtained:

Equation 70 is a quadratic which can be solved exactly for wT' to give u 2= [w(i t )-K cos wtJ-l-K cos aid] (63) wT '=wT '-K cos wio' K sin wt wm 5 V wTo At time z" the electron, having reached the plane 12, K will have traveled the distance S between planes 11 and T Sm (71) 12. This distance must be that specified by Equation 62 which, merefore, yields the: relation It may be shown that the error resultmg from the above E I t 1O mentioned approximation is of the order of 2% when e 7 1' 0') 00S O -i- K t. I K sin mid-K sin my] (64) w is not greater than 0.2; Equations 63 land 64 may be simplified by defining the The IleXt Illicessary p in {lemming '2 in terms of t it ti across gap 13 f an l t hi h l ft plane known functions is the calculation of the electron transit 11 at time t' as angle through drift space 10. This region has essentially no electric field except that due to space charge. Neglect- 1 1 0 ing this, the electrons travel through the drift space with Substituting Relation 65 into Equations 63 and 64 protheir entrance velocity expressed by Equation67. The duces transit time T1. through the drift space is, therefore,

2 Sm L 2 =(wT) +2KwT eos Cato r TIL=E 2K i Sin (66) and the transit angle is and 01L 8E0 wT' Xl2 [wT K cos w(t '+T ')+K cos wt l (67) X2 The electron transit angle when there is no alternating L Q: T/1 I( TI1) tlo) +K cos voltage present across gap 13, 1. e., the direct current wm transit angle wT may be found from Equation 66 by (72) placing K=0. LLhlSglVBS the speclal Value Equating Km 0 and substituting from Equation 68, We I 2 2 5 ascertain the average or D.-C. transit angle T 'av through 6E0 35 drift space 10 to be, Substituting this into Equation 66 and rearrangin pro- I I P duces D MT M 6 0 wL ([3) (401' |2KwT cos wt'fl-ZK sin wt' Substitution of Equation 73 and the value of wT from 2K sin w(T' -i-t' )--(wT' =0 (69) 4 Equation 71 into Equation 72 produces 2 I 2 wT' l K T an S L[wT sin wt sin w(T -l-t ()K cos (awwo] Equation 69 is a transcendental equation which cannot which is obtained by making a similar approximation to be solved directly for the instantaneous tnansit angle that employed in connection with Equation 71, viz., wT' Therefore, resort must be had at this juncture to changing T to T in the cosine term. Now, dividing approximations for which the error may be estimated. through by 'wT' and inverting by using the first term of This may be accomplished by observing that the argua binomial expression, weobtain ment of the last trigonometric term in Equation 69 con- 2 I 2 tains both T and f It is also obvious from Equation 2 il El[1+ Sin 1.. 69 that its solution will have the form L MT 0- 0 i wT =wT' +trigonometric functions of wT' and wt sin w(t '+T' cos (t 7%)] (75) w T 0 0T 0 If Variational H of '1 in P angle of the term The first factor can be simplified by substituting from 2K sin w(T +t 1n Equation 69 is neglected, T, may Equations 68 and 73 to produce be substituted for T (in this term alone) and Equation 69 becomes 'w T' K L wT'g 2S 0 T 2KT os t 2 sin I g g j ,3 whereby the instantaneous translt angle in-the drift space wT 1 becomes 65 Since we now have the instantaneous transit angle of elec- In view of the fact that the actual angle wt' at the time of arrival of an electron at plane 14 is desired for the remaining calculations, rather than the total transit angle wT' the substitution of Equations 71 and 76 into Equation 77 will not be made here. The actual angle wt, at the time of arrival of an electron at plane 14 is Equation 78 may be evaluated by substituting therein the values of QT, and wT'L from Equations 71 and 76 respectively. When this is done and the terms properly arranged, the final solution is:

where While this solution neglects the effect of space charge on the electric field, the relation for wT' including space charge effects is well known and, as adapted to nomenclature employed here, becomes where f=frequency in megacycles, S is in centimeters and V is in volts. Alternatively,

where A=wavelength in centimeters and I',,=current density in amp/cm. In the design of structures according to the invention, this corrected relation should be employed because much of the error occurring as a result of neglecting the effect of space charge in the derivation of Equation 79 may be removed in this manner.

It is now evident that substitution of the values of 1 \[1 and h from Equations 25d, 25a, and 25 respectively into Equation 25b yields a relation of the same form as Equation 79. Hence the employment of Equations 11, 54 and 79 to evaluate the integrals which define the Fourier coefficients, viz. Equations 56 and 57, yields precisely the same final relations as those determined in the foregoing general solution. We may therefore state that the output current in gap 16 is given by Equation 39 with values of p and a, termed p and a when referred specifically to the diode input case presently being discussed, determined from along with Equations 81 and 82. Thus, the results obtained in the general solution may be specifically applied to the diode input case once the functions ip' 11', and t, have been derived, thereby obviating the necessity of further analysis.

It has been shown in the foregoing general solution that optimum efficiency is obtained for cz=-1r/2 and 0=+1r/2. Equation 86 shows that for the diode input case this stipulation requires, when ot'==-1r/2 and 0'=+1r/2, that 16 The structural and operating conditions which make at: --1r/2 and 6'='+1r/ 2 may be found, therefore, by placing Equation 81 equal to zero. This then demands a value of wT',,=21r for satisfaction.

Substituting wT' =21r into Equation 82 gives L! "is is greater than one, we select the proper algebraic sign from Equation hence L! I p -K 1) is the usable form of Equation 90.

For further consideration of the diode input case as schematically illustrated in Fig. 7, it is convenient to introduce a new parameter N as follows. From Equations 68 and 73 we find aT',, L wTo' 2S (92) Defining N as 'nc N -g; (93) and substituting Equations 92 and 93 into 91 with Since we know from the foregoing general analysis that maximum efficiency at fundamental frequency occurs in the diode case when p'=p', =1.47 and M'=1.0 and since we have defined M: K, we may place these values into Equation 94 to obtain the optimum value of N as Nm=3.2 cycles (95 This means that with a and. K optimized, the electrical length of drift space 10 must be 3.2 cycles of the input frequency for maximum efficiency. Fig. 7A shows the variation of efiiciency with respect to N with a and K having their respective optimum values. At N=3.2 cycles, it will be noted that the maximum efiiciency at fundamental frequency is about 93 %the same value as that derived in the foregoing general analysis.

As has been shown heretofore p and hence p' for the diode case, decreases as the harmonic ratio n increases.

it may be seen from Equation 94 that, with one given structure, optimum bunching may be obtained over a wide range of harmonic frequencies by merely altering only the magnitude of K or, practically speaking, the magnitude of the input alternating voltage. This means that the present invention enables operation over a wide range of harmonic ratios with favorable efiiciencies. Furthermore, any of the harmonic ratios may be reached with the same structure operating at the same beam voltage by simply tuning the output resonator (in a manner more fully explained hereinafter) to the desired harmonic frequency and slightly lowering the magnitude of the input alternating voltage.

With the above teachings in mind sample calculations of actual dimensions of a diode input structure according to the invention may be illustrated. We have shown that i7 optimum performance dictates that wT' =21r. Substitutmg this into Equation 83, we obtain 21r=0.316fS( V radians (96) where f is in megacycles, S is in centimeters and V in volts. Selecting an input frequency of 1000 megacycles and a reasonable voltage of 400 volts and inserting these values into Equation 96, we have S=0.398 centimeter (97) We must now ascertain whether the Child-Langmuir space charge law gives a reasonable current density for the above assumptions. Substituting V =400 volts and S=0.398 centimeter into Equation 98, we find that which is a practical current density to expect from a conventional oxide coated cathode. When M'=l and K=%, we have learned that the optimum value of N occurs at 3.2 cycles. And from Equations 92 and '93 with wTQw=21r as hereinbefore specified for optimum efficiency, we may write =ll7 ma./cm. (99) Replacing S by its value calculated in Equation 97 we have L'=9.6S=3.82 centimeters Thus, it is clear that, knowing the frequency and beam -voltage desired, the actual dimensions of a structure according to the invention may be calculated in the above manner. .does not require the heretofore mentioned extremely And it is also clear that the present invention small interelectrode spacings of a disk-seal triode.

Referring now to Fig. 8, there is shown according tothe 'invention a diode input device comprising an input resonator 20, a drift space .21, which may be defined by a conductive non-magnetic cylinder, and an output resonator .22. Input resonator 20 includes an outerconductor .23 :and an inner conductor 24 between which is inserted a slidable tuning plunger 25. Tuning plunger '25, the position of which determines the resonant frequency of resonator 20, may comprise a plurality of circumferentiallyspaced metallic spring fingers 26 attached to rings 27 and '28 which are separated by insulating material 29. -.Rods .30 may be employed as a means of adjusting tuning plunger 25 to secure a desired resonant frequnecy of resonator 20. Electromagnetic energy may be supplied to-resonator 20 from a suitable. source (not shown) by means :of a coaxial line 31,.illustratedas capacitively coupled.

.A stream or beam of .electons may vbesupplied :tothe diode input device of the invention by an indirectly heated cathode 32 which includes a cup-shapedmember 33 having a thermionically emissive coating 34.upon the inner face thereof and a suitably supported-filament35 therewithin. .Heater current is supplied to filament 35 from a conventionallyrepresented source of direct current 36.

Drift space 21, which is essentiallyifree of electric field, comprises a conductive .hollow cylindrical portion .37 which isattached at one. extremity .toouter conductor, 23

18 of resonator 20 as indicated. Orifices 38 and 39 are provided in the input and output ends of portion 37, respectively, to permit the passage through drift space 21 of the electron stream emanating from cathode 32. Across orifices 38 and 39, respectively, are positioned electrodes illustrated as grids 40 and 41 formed of wires 42 suitably fastened to the end sections of portion 37 beyond the terminations (not shown) of the orifices. Inner conductor 24 of resonator 20, which is attached to cup-shaped member 33 by means of a flanged cylindrical member 43, terminates short of the inp'utend section of portion 37 to provide a gap 44 across which the electromagnetic field from resonator 20 may extend to supply both space charge control current modulation and velocity modulation to the electron stream emanating from cathode 32. Since the device of the invention must be evacuatedto permit electron flow, the flange of cylindrical member 43 is hermetically sealed to the input end section of portion 37 by means of a cylinder 45 of a material such as glass or ceramic. A solenoidal winding 37' supplied by a source of direct current 38' may be positioned as shown to generate a longitudinal magnetic field for focusing the electron stream.

Output resonator 22 comprises an outer conductor 46 and an inner conductor 47 between which is inserted a slidable tuning plunger 48. Tuning plunger 48 may be constructed in a manner similar to plunger 25 and may include metallic spring fingers 49, rings 50 and 51, and control rods 52. Inner conductor 47 of output resonator 22 terminates short of the output end section of portion 37 to provide an output gap 53 whereby the bunched electron stream emanating from drift space 21 may excite output resonator 22 into oscillation. Supported from a flanged circular ring 54 attached to inner conductor 47 is an anode member 55 upon which the electrons impinge after exciting output gap 53. Gap 53 is bridged by a cylindrical sealing member 56 of glass or ceramic to permit internal evacuation of the device as hereinbefore mentioned. Power may be extracted from output resonator 22 and supplied to a desired utilization circuit (not shown) by means of a concentric line 57, which is illustrated as capacitively coupled.

To supply desired operating potentials to the device of Fig. 8, there is provided a conventionally represented source of direct voltage 58 having a potentiometer 59 connected thereacross. Cathode 32 is maintained ,at an adjustably negative potential with respect to grid 40 by means of tap 60, and anode 55 is maintained at an adjustab'ly positive potential with respect to ,grid 41 by means of a tap 61 which may be connected to anode 55 as shown at 62.

It will now be understood that the device of Fig. 8 provides a means of realizing the foregoing principles of the invention. By utilizing the equations developed above, maximum efficiency israssured. The length of the input gap 44 between cathode 32 and grid 40, hereinbefore identifiedas S in the diode analysis, may be calculated from Equation 96 for a selected input frequency and beam voltage V0 which is here the voltage between the ground potential of grid 40 and the negative potential of cathode 32. After ascertaining whether the Child- Langmuir space charge law gives a reasonable current density to expect from cathode 32 .for the assumed input frequency and beam voltage, the length of drift space .21 may be calculated from Equation 101. The length-of output gap 53 and the magnitude of the;anode voltage may be selected from a rangeof values in a manner now apparent to those skilled in the art to give ,a desired efficient coupling between the bunched electron stream and output resonator 22. If it is desired to operate the device of Fig. 8 as an amplifier at fundamentalfrequency,-we

have seen that K must equal approximately /3. Hence V1, the amplitude of input signal voltage formaximum efficiency, is determined by definition ,as approximately /a. of the,magnitude of the direct voltage 1V0 across input gap 44. Both input resonator 20 and output resonator 22 are, of course, tuned to resonate at the fundamental input frequency. If it is desired to operate the identical device as a harmonic amplifier, the value of for greatest efiiciency at the selected harmonic ratio may be determined from Fig. 3 and the concomitant value of K calculated from Equation 94 with N remaining equal to 3.2 cycles of the input frequency. Output resonator 22 is then tuned to resonance at the selected harmonic frequency by means of plunger 48.

It is within contemplation of the present invention that the devices herein disclosed may be operated as generators of electromagnetic waves as well as amplifiers. The manner in which this may be accomplished is illustrated in Fig. 9 wherein numerals employed hereinbefore are used to identify like elements. In this figure a section 63 of adjustable length is shown connected to input coaxial line 31 at one end and capacitively coupled to output coaxial line 57 at the other end. Insulators 64 and 65 may be utilized to support the inner conductor 66 Within the outer conductor 67 of adjustable section 63. As will be apparent to those skilled in the art, section 63 may be arranged at the proper length to supply a desired amount of positive feedback from the output to the input of the device whereby electromagnetic oscillations are generated.

In Fig. 10, there is shown a modification of the invention particularly adaptable for operation at very high frequencies. The illustrated device comprises an input wave guide 68, a drift space 69 and an output wave guide 70. Input wave guide 68 includes a rectangular conductor 71 which is closed at its upper end and hermetically sealed at a convenient position along its length by means of a dielectric member 72. A tuning plunger 73 having an operating rod 74 extending through a hermetically sealed flexible bellows 75 is located in the upper end of wave guide 68. A plurality of flexible spring fingers 76 provide sliding contact between tuning plunger 73 and conductor 71 of wave guide 68.

A stream of electrons may be supplied to the device of Fig. by an indirectly heated cathode 77 which includes a flanged, cup-shaped member 78 having a thermionically emissive coating 79 upon the inner face thereof and a suitably supported filament 80 therewithin. Cathode 77 is insulated from conductor 71 for direct current and bypassed thereto for high frequency current by means of dielectric spacer members 81. Heating current is supplied to filament 80 from a conventionally represented source of direct current 82 connected to conductive rods 83 which are hermetically sealed to wave guide 68 by means of a dielectric spacer 84 and a box like member 85.

Drift space 69 comprises a generally rectangular portion 86 having an open end 37 which extends into input wave guide 68 and another open end 88 which extends into output wave guide 70. Across open ends 87 and 88, respectively, are positioned electrodes illustrated as grids 89 and 90 which are formed of wires 91 suitably fastened to the sides of rectangular portion 86. A solenoidal winding 92 supplied by a source of direct current (not shown) may be positioned as indicated about drift space 69 to generate a longitudinal magnetic field for focusing the electron stream which emanates from cathode 77.

-Output wave guide 70 is similar to input wave guide 68 and comprises a conductive rectangular member 93 having a tuning plunger 94 hermetically sealed into the upper end thereof. At a convenient position along its length, output wave guide 70 may be sealed from the atmosphere by a dielectric spacer element 95. An anode 96 is positioned with its inner end" adjacent grid 90 as shown and is supported in hermetically sealed relationship within the device by means of a rectangular dielectric section 97 and a flanged plate member 98. Anode 96 is insulated from wave guide 70 for direct current and 20 by-passed thereto for high frequency current by means of dielectric spacer members 99.

The operation of the device of Fig. 10 is similar to that of the device of Fig. 8, and hence will not be discussed in detail. The principles dictating prescribed operation have been set forth hereinbefore and may readily be applied by those skilled in the art. Operating voltages may be supplied to the device of Fig. 10 by means of a conventionally represented source of direct current 100, connected as shown.

In Fig. 11 there is illustrated another modification of the invention which is particularly adaptable to operation at high power levels. This modification comprises an input resonator 101, a drift space 102, and output resonators 103 and 104. Input resonator 101 is defined by an outer casing 105, an inner cylindrical member 106, a cathode 107 and a cylindrical member 108 having an inverted, somewhat T-shaped, cross section. Input power may be supplied to resonator 101 by means of a capacitively-coupled, hermetically sealed, concentric line 109. Cathode 107 comprises a pair of opposed generally circular plates 110 and 111 having a plurality of circumferentially-spaced, thermionically emissive strips 112 attached therebetween. Heater power may be supplied to cathode 107 from a conventionally represented source of direct current 113 through a rigid conductor 114 secured to plate 111. At the inner terminus of drift space 102, an electrode illustrated as a grid 115 formed of a plurality of circumferentially spaced wires 116, is positioned. At their respective ends wires 116 are attached to conductive cylinders 117 and 118, the former of which is ca pacitively by-passed to a boss 119 of casing 105 by a dielectric cylinder 120. Conductive cylinder 113 is capacitively by-passed to a boss 121 of casing 105 by a dielectric cylinder 122 and is also capacitively by-passe'd to cylindrical member 108 by a dielectric cylinder 123. Drift space 102 extends radially from the inner ends of bosses 119 and 121 to output gaps 124 and 125 in output resonators 103 and 104, respectively. Power may be extracted from output resonators 103 and 104, which are coupled together through their electromagnetic fields, by means of a magnetically coupled, hermetically sealed coaxial line 126. To increase the power range of the device, a suitable coolant may be circulated through a cylindrical space 127 in casing 105.

In operation the device of Fig. 11 has similar char acteristics to the devices of Figs. 8 and 10 with the exception that electrode 115 provides a triode input to drift space 102 for a purpose which will be more fully explained later in connection with the device of Fig. l2. Electrons emanating from cathode 107 are affected by the electromagnetic field within input resonator 101 and are given both space charge control and velocity modulation components in the gap between cathode 107 and grid 115. After the bunched electrons cross gaps 124 and 125 to excite output resonators 103 and 104, they are discharged upon an anode portion 128 of casing 105. Operating potentials may be supplied to the device of Fig. 11 from a conventionally represented source of direct voltage 129, the positive terminal of which is maintained at the same potential as casing 105. Cathode 107 is maintained at an adjustably negative potential with respect to anode 28 by means of a conductor 129', while grid 115 is held at an adjustably negative potential with respect to cathode 107 by means of a conductor 130 which is hermetically introduced into the device as illustrated.

In certain instances, it may be desirable to have some flexibility with regard to the selection of beam voltage for the device of the invention. From the foregoing discussion in connection with Fig. 8, it will be observed that one particular value of beam voltage V0 is assumed, along with the desired frequency of operation, and the remainder of the parameters for the device then calcu lated from the derived equations. In the device illustrated in Fig. 12, wherein numerals utilized hereinbefore are employed to identify like elements, therev is provided a triod'e input to drift space 21 for the purposeof obtaining maximum efficiency over a wide range of values for thebeam voltage. The device of Fig. 12 comprises an electrode shown in the form of a grid 135 inserted between cathode 32 and electrode 40. Grid 135 is formedof transversely extending Wires 136 attached to a flanged conductive washer 137 which extends through dielectric cylinder 45. Washer 137 is conductively connected to a washer 138 through spring fingers 139, and washer 138 is by-passed to input resonator 20 and drift space 21 by means of dielectric washers 140 and 141, respectively. It will now be observed that by maintaining grid 135 at an adjustably negative potential with respect to cathode 32 by means of a tap 142, various values of beam voltage may be selected in conjunction with the voltage of grid 135 to achieve maximum efliciency in accordance with the foregoing principles of the invention. With the insertion of grid 135, the average transit time of electrons across the input gap becomes a function of both the voltage of grid 135 and the beam voltage. Hence, a great number of combinations of these voltages is available without the sacrifice of efficiency. Specific attention is directed to the fact that the electromagnetic fields from resonator 20 are applied between cathode 32 and grid 135 to obtain the desired space charge control and velocity modulation in the embodiment of Fig. 12.

Obviously, the feedback means illustrated in Fig. 9 or means equivalent thereto may be employed with all the various embodiments of the invention to obtain a high frequency oscillator. Furthermore, the output waves transducing means in the various embodiments of the invention, i. e., the resonators and wave guides, may be tuned to a harmonic of the frequency to which the input wave transducing means is tuned. to obtain a high efficiency harmonic amplifier. Also, in the embodiments of Figs. 11 and 12, low frequency modulation voltages may be applied respectively to electrodes 115 and 135 in well known ways to insert intelligence signals into the devices.

From the foregoing it is manifest that the present invention provides methods and devices in which the translation of electromagnetic energy is accomplished in novel manner with very high efficiency. The application of both space charge control and velocity modulation components to an electron stream according to the invention may be accomplished with a variety of input electrode structures. Selection of a desired input electrode structure enables determination of the various parameters by means of the equations developed herein. As an example, detailed calculations for a diode input structure have been included in the above description. Thus, by utilization of the instant invention, new and improved methods of and devices for the generation and amplification of electromagnetic waves are realized.

While the present invention has been described by reference to particular embodiments thereof, alternative constructions will readily occur to those skilled in the art. It is therefore intended, in the appended claims, to cover all such equivalent embodiments as may be within the true spirit and scope of the foregoing description.

What I claim as new and desire to secure by Letters Patent of the United States is:

1. An electron discharge device system of the type employing an electron beam comprising a cathode for generating a beam of electrons, means providing a drift space spaced along said beam from said cathode to provide an input gap, electromagnetic wave transducing means coupled to said electron beam in said input gap to supply high frequency fields for modulating said electron beam with a space charge control component, electromagnetic wave transducing means coupled to said electron beam in said input gap to supply high frequency fields for modulating said electron. beam with av velocity modulation cont ponent, the total transit angle of. electrons fromsaid cathode to the exit end of said drift spacehaving a phase angle of about +1r/2 with respect to saidspace charge component, an anode spaced from said exit end. of said drift space, and, output electromagnetic wave transducing means coupled with said electron beam in the space between the exit endof said drift space and said anodefor deriving electromagnetic energy'from said electron beam.

2. An electron discharge device system of the type employing an electron beam comprising a cathode for generating a beam of electrons, means-providing a drift space spaced along said beam from said cathode to provide an input gap, electromagnetic wave transducing-means coupled to said electron beam in said input gap to supply high frequency fields for modulating said electron. beam with a space charge control component, electromagnetic wave transducing means coupled to'said electron beam in said input gap to supply high frequency fields for modulating said electron beam with a;velocity-modulation'com ponent, the total transit angle. of electrons from said;

cathode to said exit end of said drift space having a phase angle of approximately +1r/2 with respect to said space charge component, said electron beam emerging from said drift space representing an alternating current having a magnitude Cn determined by the relation where in is the direct current'represented by the electron.

beam, in is a Bessel function of the firstkind, n is any; integer, p is a bunching parameter dependent upon the magnitude of the velocity modulation component andthe length of said drift space, and M is a modulationindex of the space charge control component, an anode spaced from said exit end of said drift space, and output electromagnetic wave transducing means coupled with said-electron beam in the spacebetween the exit end-ofsaiddrift space and said anode for deriving electromagnetic energy from said electron beam.

3. A system as in claim 2 in which said bunching factor p has a value of about 1.47.

4. A system as in claim 2 in which said modulation index M has a value of about 1'.

5. A system as in claim 2 in which said. bunching parameter p is selected from the range of about 0.7 to 2.0 and said modulation index M has a valueof about. 1.

6. An electron discharge devicesystem of the type employing an electron beam comprising a cathode for generating a beamuof electrons, means providing a drift space spaced along said beam. from said cathode to provide an input gap, said means including a hollow conductivemember' maintained at a positive potential with respect to said cathode for accelerating said electron beam in said input gap, a cavity resonator connected for high frequency cur= rents between said cathode and said hollow conductive member to supply high frequency fields across said gap for modulating said electron beam with both space charge control and velocity modulation components, said gap having a length equal to an average transit angle of the electrons in the beam 2, an anode spaced from the end of said drift space remote from said cathode, and a cavity resonator coupled with said electron beam in the space 9. A system as in claim 7 in which p is approximately quency fields supplied by said first recited cavity resonator.

10. An electron discharge device system of the type employing an electron beam comprising a cathode for generating a beam of electrons, means providing a drift space spaced along said beam from said cathode to provide an input gap, said means including a hollow conductive member maintained at a positive potential with respect to said cathode for accelerating said electron beam in said input gap, a wave guide connected for high frequency currents between said cathode and said hollow conductive member to supply high frequency fields for modulating said electron beam with both space charge control and velocity modulation components, said input gap having an electrical length of 21r at the operating frequency for the positive potential applied to said hollow conductive member an anode spaced from the end of said drift space remote from said cathode, and a wave guide coupled with said electron beam in the space between said end of said drift space and said anode for deriving electromagnetic energy from said electron beam.

11. An electron discharge device system of the type employingan electron beam comprising a cathode for generating a beam of electrons, means providing a drift space spaced along said beam from said cathode to provide an input gap, said means including a hollow conductive member maintained at a positive potential with respect to said cathode for accelerating said electron beam in said input gap, a wave guide connected for high frequency currents between said cathode and said hollow conductive member to supply high frequency fields for modulating said electron beam with both space charge control and velocity modulation components, said input gap having an electrical length of 211- at the operating frequency for the positive potential applied to said hollow conductive member an anode spaced from the end of said drift space remote from said cathode, a wave guide coupled with said electron beam in the space between said end of said drift space and said anode for deriving electromagnetic energy from said electron beam, and feedback means intercoupling said wave guides for sustaining oscillations in said device.

. 12. A device system as in claim 10 in which said first recited wave guide is tuned to a predetermined input frequency and said second recited device is tuned to a harmonic of said predetermined input frequency.

13. An electron discharge device system of the type employing an electron beam comprising a cathode for generating a beam of electrons, means providing a drift space the entrance end of which is spaced along said beam a predetermined distance from said cathode, an electron permeable electrode positioned traversing said beam between said cathode and said entrance end of said drift space, electromagnetic wave transducing means connected for high frequency currents between said cathode and said electron permeable electrode to supply high frequency fields for modulating said electron beam with both space charge control and velocity modulation components, the total transit angle of electrons from said cathode to the entrance end of said drift space having a phase angle of about generating a beam of electrons, means providing a drift 24 including a hollow conductive member maintained at a positive potential with respect to said cathode for accelerating said electron beam, an electron permeable electrode positioned traversing said electron beam between said cathode and said entrance end of said drift space, electromagnetic wave transducing means connected for high.

frequency currents between said cathode and said electron permeable electrode to supply high frequency fields for modulating said electron beam with both space charge control and velocity modulation components, the total transit angle of electrons from said cathode to the entrance end of said drift space having a phase angle of about with respect to said space charge component, an anode spaced from the exit end of said drift space, and electromagnetic wave transducing means coupled with said electron beam in the space between said exit end of said drift space and said anode for deriving electromagnetic energy from said electron beam.

15. A device system as in claim 14 in which each of said electromagnetic wave transducing means comprises a cavity resonator.

16. A device system as in claim 14 in which said electron permeable electrode is maintained at a negative potential with respect to said cathode.

17. A device system as in claim 14 in which said first recited electromagnetic wave transducing means is tuned to a predetermined input frequency and said second recited electromagnetic wave transducing means is tuned to a harmonic of said input frequency.

18. An electron discharge device system of the type employing an electron beam comprising a cathode for generating a beam of electrons, means providing a drift space the entrance end of which is spaced along said beam a predetermined distance from said cathode, said means including a hollow conductive member maintained at a positive potential with respect to said cathode forv accelerating said electron beam, an electron permeable electrode positioned traversing said electron beam between said cathode said entrance end of said drift space,

electromagnetic wave transducing means connected for high frequency currents between said cathode and said electron permeable electrode to supply high frequency fields for modulating said electron beam with both space charge control and velocity modulation components, the the total transit angle of electrons from said cathode to the entrance end of said drift space having a phase angle of about fining wall thereof, a cathode positioned within said resonator opposite said opening for generating a beam of electrons which passes through said opening, means providing a drift space for said electron beam having said opening as an entrance end, and an annular cavity resonator coupled with said electron beam at the exit end of said drift space the total transit angle of-electrons from said 25 cathode to the entrance end of said drift space having a phase angle of about with respect to said space charge component.

20. An electron discharge device system of the type employing an electron beam comprising a cylindrical cavity resonator having a peripheral opening in the defining wall thereof, a cylindrical cathode positioned within said resonator opposite said opening for generating a beam of electrons which passes through said opening, an electron permeable grid positioned traversing said beam of electrons between said cathode and said opening such that electromagnetic waves sustained within said cavity resonator modulate said electron beam with both space charge control and velocity modulation in the space between said cathode and said grid, means providing a drift space for said electron beam having said opening as an entrance end, an annular cavity resonator coupled with said electron beam at the exit end of said drift space to extract electromagnetic energy from said beam the total transit angle of electrons from said cathode to the entrance end of said drift space having a phase angle of about with respect to said space charge component.

21. A device system in claim 20 in which said defining wall of said cavity resonator is maintained at a positive potential with respect to said cathode and said electron 26 permeable grid is maintained at a negative potential with respect to said cathode.

22. A device system as in claim 21 in which said electron permeable grid is by-passed for high frequency currents to said defining wall of said cavity resonator.

23. An electron discharge device system of the type employing an electron beam comprising a cathode and generating a beam of electrons, means spaced from said cathode and providing a drift space spaced along said beam from said cathode to provide an input gap, electromagnetic wave transducing means coupled to said electron beam to supply high frequency fields across said input gap for modulating said beam with a space charge control component and a velocity modulation component, the physical length of said gap corresponding to an average transit angle of electrons across said gap of Zn, an anode spaced from the exit end of said drift space, and output electromagnetic wave transducing means coupled with said electron beam in the space between the exit end of said drift space and said anode for deriving electromagnetic energy from said electron beam.

References Cited in the file of this patent UNITED STATES PATENTS Re. 22,580 Mouromtseff et al Dec. 19, 1944 Re. 22,389 Litton Nov. 2, 1943 2,314,794 Linder Mar. 23, 1943 2,368,031 Llewellyn Jan. 23, 1945 2,391,016 Ginzton et al. Dec. 18, 1945 2,425,748 Llewellyn Aug. 19, 1947 2,484,643 Peterson Oct. 11, 1949 2,498,886 Hahn Feb. 28, 1950 

